Question

Bonny's truck has a fuel tank which holds 50 gallons, and she typically drives 425 miles on a full tank. She has added a second tank, which holds 30 gallons. To figure how far she can go between fill-ups now, she multiplies 50 x 425, then divides by 30, to get 708.3 miles. Is this correct?

A) Yes.
B) No; she should have multiplied 425 by 30 + 50.
C) No; she should have divided 425 by 50, then multiplied by 80.
D) No; she should have divided 50 by 30, then multiplied that by 425.


SHOW WORK!!

Answer 1

Firstly, let's solve the question.
50 gallons : 425 miles
30 gallons : x miles

You can use cross multiplication, but I personally prefer ratios because they make more sense in my head.
50 : 425 simplified is 1 : 8.5
To find the miles for 30 gallons, each side is multiplied by 30
30 : 255

Or:
30*425=12,750
12,750/50= 255

255+425=680 miles, which is the total distance she can travel without refilling.
A) Her answer isn't 680, so this isn't your answer
B) 425*30= 12,750 + 50 = 12,800 (Wrong)
C) 425/50 = 8.5*80 = 680 (Correct)
D) 50/30 = 1.6 recurring*425 = 708.3 recurring (Wrong)

I'm not sure where those numbers came from, but the only option that gives the correct answer is C.

Answer 2

This is the perfect place to use a proportion:

Old capacity . . . 50 gallons
Old distance . . . 425 miles

New capacity . . . (50 + 30) = 80 gallons
New distance . . .  D

The proportion:
                                            425 / 50         =  D / 80  .


Multiply each side by  80 :  425 x 80 / 50  =  D

                                                     680       =  D .